A while ago I played around with the Collatz conjecture a bit myself. I guess this is all well-known but maybe some people find it interesting: One thing I not

A while ago I played around with the Collatz conjecture a bit myself. I guess this is all well-known but maybe some people find it interesting: One thing I noticed was that the seemingly chaotic directed graph can be ordered if you arrange the integers in a two dimensional grid where the x axis is the uneven numbers and each row doubles the previous one. So like: 1 3 5 7 9 ... 2 6 10 14 18 4 12 20 28 36 .. It's clear to see that if n ≡ 0 (mod 2) we'll be on some row other than the first so we'd just move all the way to the top. For integers on the first row there's some interesting "orbits" forming[1]. You can categorize them by which 2^n row the 3n+1 rule will jump to and each of those will attract to some specific position the 2^1 and 2^2 ones seem to be the only ones with an integer center point (at 1 and -1 respectively, so that's where you have cycles). Another interesting pattern I've noticed (not really shown) is that "combined" jumps like "first a jump into the 2^1 row followed by a jump into the 2^2 row" also follow these fixed intervals. [1] https://raw.githubusercontent.com/gist/ginkgo/7120618db058d6280d7bf9ea0b8db4e1/raw/27bba3b9ba409375ce1b7819849762e29647ae1e/collatz_grid.svg https://raw.githubusercontent.com/gist/ginkgo/7120618db058d6...